Nuprl Lemma : decidable__existse-between1

es:EO. ∀e1,e2:E.
  ∀[P:{e:E| loc(e) loc(e1) ∈ Id}  ─→ ℙ]. ∀e@loc(e1).Dec(P[e])  Dec(∃e∈[e1,e2).P[e]) supposing loc(e2) loc(e1) ∈ Id


Proof




Definitions occuring in Statement :  existse-between1: e∈[e1,e2).P[e] alle-at: e@i.P[e] es-loc: loc(e) es-E: E event_ordering: EO Id: Id decidable: Dec(P) uimplies: supposing a uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] implies:  Q set: {x:A| B[x]}  function: x:A ─→ B[x] equal: t ∈ T
Lemmas :  alle-at_wf Id_wf es-loc_wf es-E_wf decidable_wf equal_wf event_ordering_wf decidable__existse-before es-le_wf decidable__and decidable__es-le es-locl_wf es-le-loc not_wf exists_wf
\mforall{}es:EO.  \mforall{}e1,e2:E.
    \mforall{}[P:\{e:E|  loc(e)  =  loc(e1)\}    {}\mrightarrow{}  \mBbbP{}]
        \mforall{}e@loc(e1).Dec(P[e])  {}\mRightarrow{}  Dec(\mexists{}e\mmember{}[e1,e2).P[e])  supposing  loc(e2)  =  loc(e1)



Date html generated: 2015_07_17-AM-08_47_33
Last ObjectModification: 2015_01_27-PM-02_28_06

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